RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.69 21.9296 0.812558 2 to 25 15.66 24.7889 0.900465 3 to 26 16.08 17.7664 0.596282 4 to 27 15.79 23.0575 0.852611 5 to 28 15.94 14.9283 0.399357 6 to 29 15.99 13.1050 0.270873 7 to 30 15.81 11.7562 0.185331 8 to 31 15.40 28.3602 0.959099 9 to 32 15.52 14.9433 0.400437 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.501923 Tough bday spacings test for dh-ranFile-2018-07-05_22:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 10 33 69 103 94 79 59 27 11 5 10 (O-E)^2/E 0.1 0.4 0.2 0.3 0.1 0.0 0.9 0.3 1.0 0.4 8.7 Birthday Spacings: Sum(O-E)^2/E= 12.363, p= 0.739 RESULTS OF GCD FOR dh-ranFile-2018-07-05_22:31 Euclid's algorithm: p-value, steps to gcd: 0.543236 p-value, dist. of gcd's: 0.514224 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.794 0.754 0.898 0.555 0.964 0.398 0.959 0.028 Bits 8 to 15---> 0.467 0.456 0.220 0.672 0.016 0.073 0.203 0.402 Bits 16 to 23---> 0.972 0.759 0.341 0.716 0.187 0.735 0.885 0.585 Bits 24 to 31---> 0.737 0.095 0.646 0.811 0.560 0.503 0.282 0.444 KS test for the above 32 p values: 0.159 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_22:31, p-values for 5 runs: 0.5329, 0.7466, 0.5289, 0.3110, 0.1685 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5151 5134.0 0.056 1.039 r= 30 23103 23103.0 0.000 1.039 r= 31 11549 11551.5 0.001 1.040 chi-square = 1.040 with df = 3; p-value = 0.208 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5200 5134.0 0.848 1.578 r= 31 23073 23103.0 0.039 1.617 r= 32 11528 11551.5 0.048 1.665 chi-square = 1.665 with df = 3; p-value = 0.355 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_22:31 b-rank test for bits 1 to 8, p=0.26631 b-rank test for bits 2 to 9, p=0.60700 b-rank test for bits 3 to 10, p=0.53110 b-rank test for bits 4 to 11, p=0.73561 b-rank test for bits 5 to 12, p=0.91522 b-rank test for bits 6 to 13, p=0.92820 b-rank test for bits 7 to 14, p=0.40007 b-rank test for bits 8 to 15, p=0.48693 b-rank test for bits 9 to 16, p=0.69401 b-rank test for bits 10 to 17, p=0.34634 b-rank test for bits 11 to 18, p=0.28981 b-rank test for bits 12 to 19, p=0.27833 b-rank test for bits 13 to 20, p=0.13108 b-rank test for bits 14 to 21, p=0.16238 b-rank test for bits 15 to 22, p=0.66168 b-rank test for bits 16 to 23, p=0.91738 b-rank test for bits 17 to 24, p=0.78678 b-rank test for bits 18 to 25, p=0.08926 b-rank test for bits 19 to 26, p=0.34936 b-rank test for bits 20 to 27, p=0.38031 b-rank test for bits 21 to 28, p=0.78037 b-rank test for bits 22 to 29, p=0.96059 b-rank test for bits 23 to 30, p=0.20078 b-rank test for bits 24 to 31, p=0.27139 b-rank test for bits 25 to 32, p=0.68632 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.859950 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_22:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 142492 1.36 0.913303 2 141980 0.17 0.565574 3 141749 -0.37 0.353978 4 141888 -0.05 0.480126 5 141575 -0.78 0.217359 6 141763 -0.34 0.366216 7 141988 0.18 0.572918 8 141763 -0.34 0.366216 9 141487 -0.99 0.161882 10 142558 1.52 0.935188 11 142128 0.51 0.695293 12 142136 0.53 0.701806 13 142435 1.23 0.890314 14 141953 0.10 0.540635 15 142625 1.67 0.952750 16 141608 -0.70 0.240703 17 142199 0.68 0.750733 18 141423 -1.14 0.127919 19 141903 -0.01 0.494100 20 141729 -0.42 0.336756 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-05_22:31 Bits used No. missing words z-score p-value 23 to 32 141662 -0.8529 0.196868 22 to 31 141708 -0.6942 0.243765 21 to 30 142080 0.5885 0.721907 20 to 29 141827 -0.2839 0.388245 19 to 28 141707 -0.6977 0.242686 18 to 27 142642 2.5264 0.994239 17 to 26 142106 0.6782 0.751169 16 to 25 141538 -1.2804 0.100194 15 to 24 142305 1.3644 0.913776 14 to 23 142194 0.9816 0.836857 13 to 22 141816 -0.3218 0.373792 12 to 21 141995 0.2954 0.616161 11 to 20 141854 -0.1908 0.424344 10 to 19 141846 -0.2184 0.413567 9 to 18 142013 0.3575 0.639635 8 to 17 141881 -0.0977 0.461089 7 to 16 142251 1.1782 0.880636 6 to 15 141838 -0.2460 0.402855 5 to 14 141967 0.1989 0.578815 4 to 13 142216 1.0575 0.854854 3 to 12 141776 -0.4598 0.322845 2 to 11 141529 -1.3115 0.094847 1 to 10 141926 0.0575 0.522920 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-05_22:31 Bits used No. missing words z-score p-value 28 to 32 142266 1.2091 0.886678 27 to 31 141886 -0.0791 0.468483 26 to 30 141913 0.0124 0.504963 25 to 29 142022 0.3819 0.648744 24 to 28 142018 0.3684 0.643702 23 to 27 141936 0.0904 0.536018 22 to 26 142491 1.9718 0.975682 21 to 25 142325 1.4091 0.920590 20 to 24 141960 0.1718 0.568188 19 to 23 141795 -0.3876 0.349171 18 to 22 141797 -0.3808 0.351683 17 to 21 141938 0.0972 0.538711 16 to 20 141486 -1.4350 0.075641 15 to 19 141641 -0.9096 0.181519 14 to 18 142087 0.6023 0.726503 13 to 17 142043 0.4531 0.674768 12 to 16 142132 0.7548 0.774820 11 to 15 141900 -0.0316 0.487385 10 to 14 141996 0.2938 0.615543 9 to 13 142479 1.9311 0.973264 8 to 12 141573 -1.1401 0.127122 7 to 11 141852 -0.1943 0.422955 6 to 10 141365 -1.8452 0.032505 5 to 9 142418 1.7243 0.957674 4 to 8 141756 -0.5198 0.301615 3 to 7 141984 0.2531 0.599912 2 to 6 141721 -0.6384 0.261605 1 to 5 140984 -3.1367 0.000854 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-05_22:31 Bits used No. missing words z-score p-value 31 to 32 141864 -0.1337 0.446813 30 to 31 141325 -1.7237 0.042382 29 to 30 142051 0.4179 0.661992 28 to 29 141518 -1.1544 0.124175 27 to 28 142326 1.2291 0.890486 26 to 27 141852 -0.1691 0.432853 25 to 26 141811 -0.2901 0.385886 24 to 25 142373 1.3678 0.914306 23 to 24 142081 0.5064 0.693713 22 to 23 141950 0.1200 0.547747 21 to 22 141728 -0.5349 0.296361 20 to 21 141928 0.0551 0.521960 19 to 20 142249 1.0020 0.841823 18 to 19 142133 0.6598 0.745307 17 to 18 141191 -2.1190 0.017047 16 to 17 141448 -1.3609 0.086780 15 to 16 142673 2.2527 0.987861 14 to 15 141587 -0.9508 0.170846 13 to 14 141841 -0.2016 0.420129 12 to 13 141355 -1.6352 0.051004 11 to 12 141427 -1.4228 0.077397 10 to 11 142033 0.3648 0.642373 9 to 10 141728 -0.5349 0.296361 8 to 9 142596 2.0256 0.978596 7 to 8 141819 -0.2665 0.394942 6 to 7 142217 0.9076 0.817950 5 to 6 142819 2.6834 0.996356 4 to 5 141832 -0.2281 0.409780 3 to 4 142220 0.9164 0.820280 2 to 3 141662 -0.7296 0.232821 1 to 2 141752 -0.4641 0.321288 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2541.64 0.589 0.722042 Test results for specific bytes for dh-ranFile-2018-07-05_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2512.47 0.176 0.569993 2 to 9 2527.01 0.382 0.648784 3 to 10 2566.24 0.937 0.825565 4 to 11 2639.29 1.970 0.975576 5 to 12 2334.97 -2.334 0.009799 6 to 13 2606.95 1.512 0.934793 7 to 14 2523.70 0.335 0.631253 8 to 15 2505.86 0.083 0.533011 9 to 16 2519.86 0.281 0.610617 10 to 17 2545.81 0.648 0.741457 11 to 18 2586.98 1.230 0.890657 12 to 19 2519.59 0.277 0.609151 13 to 20 2411.38 -1.253 0.105045 14 to 21 2539.34 0.556 0.711023 15 to 22 2542.40 0.600 0.725612 16 to 23 2488.03 -0.169 0.432797 17 to 24 2464.99 -0.495 0.310281 18 to 25 2465.79 -0.484 0.314258 19 to 26 2374.19 -1.779 0.037600 20 to 27 2404.19 -1.355 0.087716 21 to 28 2623.07 1.740 0.959108 22 to 29 2457.54 -0.600 0.274095 23 to 30 2499.64 -0.005 0.497972 24 to 31 2463.82 -0.512 0.304420 25 to 32 2509.01 0.127 0.550693 CDPARK for dh-ranFile-2018-07-05_22:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3555 1.4612 0.928018 3532 0.4110 0.659449 3527 0.1826 0.572463 3533 0.4566 0.676028 3546 1.0502 0.853193 3525 0.0913 0.536383 3509 -0.6393 0.261324 3547 1.0959 0.863437 3536 0.5936 0.723613 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3533.10 sample std.=12.96 p-value of the KSTEST for those 10 p-values: 0.129159 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_22:31 0.8747,0.8498,0.2477,0.5207,0.2720,0.3784,0.1108,0.0375,0.1784,0.4595, The KS test for those 10 p-values: 0.428403 The 3DSPHERES test for dh-ranFile-2018-07-05_22:31 sample no r^3 equiv. uni. 1 47.560 0.795121 2 17.294 0.438125 3 86.454 0.943967 4 52.992 0.829054 5 15.202 0.397542 6 12.312 0.336609 7 10.644 0.298676 8 97.686 0.961466 9 14.534 0.383966 10 3.338 0.105307 11 48.125 0.798940 12 37.358 0.712136 13 43.111 0.762369 14 7.477 0.220613 15 6.622 0.198068 16 10.286 0.290262 17 54.164 0.835604 18 10.537 0.296174 19 10.572 0.296995 20 42.277 0.755672 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.515651 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.1 0.5 -0.3 -0.6 -0.6 -1.2 -0.9 -1.4 -0.1 1.9 0.4 1.5 -0.3 -0.1 -0.2 -0.6 0.6 -1.7 0.1 -0.3 0.0 -0.4 0.1 1.9 0.3 0.3 1.3 0.4 -0.1 0.8 -2.0 -0.2 -0.8 0.1 -0.9 -0.1 0.1 -0.7 0.1 2.0 -0.1 Chi-square with 42 degrees of freedom:32.260559 z-score=-1.062660, p-value=0.139235 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-05_22:31 Test no p-value 1 0.013228 2 0.669571 3 0.258005 4 0.291125 5 0.890826 6 0.020028 7 0.928158 8 0.557882 9 0.368802 10 0.777949 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.673268 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_22:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66913 0.91 66770 0.16 3 25000.00 24710 3.36 25069 0.19 4 6666.67 6679 0.02 6539 2.44 5 1388.89 1410 0.32 1350 1.09 6 238.10 245 0.20 225 0.72 7 34.72 39 0.53 38 0.31 8 4.96 3 0.77 8 1.86 p=0.59014 p=0.65812 Number of rngs required: 687389, p-value: 0.119 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_22:31 No. of wins: Observed Expected 98235 98585.9 z-score=-1.569, pvalue=0.05830 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66675 66666.7 0.001 0.001 2 37455 37654.3 1.055 1.056 3 26950 26954.7 0.001 1.057 4 19249 19313.5 0.215 1.272 5 13937 13851.4 0.529 1.801 6 10063 9943.5 1.435 3.236 7 7195 7145.0 0.350 3.586 8 5105 5139.1 0.226 3.811 9 3762 3699.9 1.043 4.855 10 2635 2666.3 0.367 5.222 11 1974 1923.3 1.335 6.557 12 1371 1388.7 0.227 6.784 13 1010 1003.7 0.039 6.823 14 716 726.1 0.142 6.965 15 500 525.8 1.269 8.234 16 381 381.2 0.000 8.234 17 283 276.5 0.151 8.385 18 196 200.8 0.116 8.501 19 148 146.0 0.028 8.529 20 101 106.2 0.256 8.785 21 294 287.1 0.165 8.950 Chisq= 8.95 for 20 degrees of freedom, p= 0.01653 SUMMARY of craptest p-value for no. of wins: 0.058296 p-value for throws/game: 0.016525 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_22:31 No. of wins: Observed Expected 98205 98585.9 z-score=-1.703, pvalue=0.04424 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66637 66666.7 0.013 0.013 2 37468 37654.3 0.922 0.935 3 27149 26954.7 1.400 2.335 4 19182 19313.5 0.895 3.230 5 13979 13851.4 1.175 4.405 6 9979 9943.5 0.126 4.532 7 7223 7145.0 0.851 5.383 8 5104 5139.1 0.239 5.622 9 3690 3699.9 0.026 5.648 10 2666 2666.3 0.000 5.648 11 1994 1923.3 2.597 8.245 12 1450 1388.7 2.702 10.947 13 961 1003.7 1.818 12.765 14 670 726.1 4.340 17.106 15 520 525.8 0.065 17.170 16 378 381.2 0.026 17.196 17 228 276.5 8.520 25.716 18 191 200.8 0.481 26.197 19 140 146.0 0.245 26.443 20 114 106.2 0.571 27.013 21 277 287.1 0.356 27.370 Chisq= 27.37 for 20 degrees of freedom, p= 0.87482 SUMMARY of craptest p-value for no. of wins: 0.044245 p-value for throws/game: 0.874816 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0098,0.0132,0.0159,0.0165,0.0170,0.0200,0.0283,0.0325,0.0375, 0.0376,0.0424,0.0442,0.0510,0.0583,0.0734,0.0756,0.0774,0.0868,0.0877, 0.0893,0.0948,0.0950,0.1002,0.1050,0.1053,0.1108,0.1194,0.1242,0.1271, 0.1279,0.1292,0.1311,0.1392,0.1592,0.1619,0.1624,0.1685,0.1708,0.1784, 0.1815,0.1853,0.1869,0.1969,0.1981,0.2008,0.2029,0.2084,0.2174,0.2201, 0.2206,0.2328,0.2407,0.2427,0.2438,0.2477,0.2580,0.2613,0.2616,0.2663, 0.2709,0.2714,0.2720,0.2741,0.2783,0.2817,0.2898,0.2903,0.2911,0.2962, 0.2964,0.2964,0.2970,0.2987,0.3016,0.3044,0.3103,0.3110,0.3143,0.3213, 0.3228,0.3366,0.3368,0.3411,0.3463,0.3492,0.3494,0.3517,0.3540,0.3552, 0.3662,0.3662,0.3688,0.3738,0.3784,0.3803,0.3840,0.3859,0.3882,0.3949, 0.3975,0.3976,0.3994,0.4001,0.4004,0.4025,0.4029,0.4098,0.4136,0.4201, 0.4230,0.4243,0.4284,0.4328,0.4329,0.4381,0.4436,0.4468,0.4558,0.4595, 0.4611,0.4636,0.4675,0.4685,0.4801,0.4869,0.4874,0.4941,0.4980,0.5019, 0.5031,0.5050,0.5142,0.5157,0.5207,0.5220,0.5229,0.5289,0.5311,0.5329, 0.5330,0.5360,0.5364,0.5387,0.5406,0.5432,0.5477,0.5507,0.5548,0.5579, 0.5601,0.5656,0.5682,0.5700,0.5725,0.5729,0.5788,0.5854,0.5901,0.5963, 0.5999,0.6070,0.6092,0.6106,0.6155,0.6162,0.6313,0.6396,0.6424,0.6437, 0.6463,0.6487,0.6488,0.6581,0.6594,0.6617,0.6620,0.6696,0.6715,0.6733, 0.6748,0.6760,0.6863,0.6937,0.6940,0.6953,0.7018,0.7110,0.7121,0.7156, 0.7219,0.7220,0.7236,0.7256,0.7265,0.7350,0.7356,0.7366,0.7385,0.7415, 0.7453,0.7466,0.7507,0.7512,0.7537,0.7557,0.7586,0.7624,0.7748,0.7779, 0.7804,0.7868,0.7937,0.7951,0.7989,0.8112,0.8126,0.8180,0.8203,0.8256, 0.8291,0.8356,0.8369,0.8418,0.8498,0.8526,0.8532,0.8549,0.8600,0.8634, 0.8747,0.8748,0.8806,0.8853,0.8867,0.8903,0.8905,0.8907,0.8908,0.8984, 0.9005,0.9133,0.9138,0.9143,0.9152,0.9174,0.9206,0.9280,0.9282,0.9282, 0.9348,0.9352,0.9440,0.9528,0.9577,0.9585,0.9591,0.9591,0.9606,0.9615, 0.9643,0.9720,0.9733,0.9756,0.9757,0.9786,0.9879,0.9942,0.9964, Overall p-value after applying KStest on 269 p-values = 0.681673 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.